M. Ramzan

PROPER CURVATURE COLLINEATIONS IN NONSTATIC SPHERICALLY SYMMETRIC SPACE–TIMES

A study of nonstatic spherically symmetric space–times according to their proper curvature collineations is given by using the rank of the 6×6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in each case of the above space–times it is shown that when the above space–times admit proper curvature collineations, they turn out to be static spherically symmetric and form an infinite dimensional vector space. In the nonstatic cases curvature collineations are just Killing vector fields.

A note on proper curvature collineations in Bianchi type VIII and IX space-times

We investigate proper curvature collineations in Bianchi type VIII and IX space-times using the rank of the 6 x 6 Riemann matrix and direct integration techniques. We found only one case when the above space-times become static and admit proper curvature collineations which form an infinite-dimensional vector space.